How to calculate standard errors/fitting errors of parameters in Linear and Nonlinear Regression?

Once we estimate the parameters, I read that the standard errors associated with each parameter is given by

,

where Covariance Matrix is given by

, for Multiple Linear Regression and

, for Nonlinear Regression - Levenberg-Marquardt algorithm.

Here n is the number of observations and p is the number of parameters.

I would like to know if the above formulae are correct.

Why aren't the errors associated with the parameters not dependent of the value of alpha (number of standard deviations, eg: 0.5) ?